This invention relates to the field of nonlinear controllers and is particularly adapted to augment conventional Proportional-Integral-Derivative (PID) controllers so that they function more effectively for controlling time varying dynamic processes and systems.
Controllers are inherently complex since they control dynamically changing systems, trying to match a desired response with the system output. (The desired response can be a setpoint change or the output curve of a reference model exhibiting the desired response characteristics.) In most real control situations, one would not expect, and cannot achieve, the process output being brought to setpoint instantaneously. Therefore, following the presumed optimal curve is the goal.
Both by virtue of and despite their simplicity, linear controllers continue to be the workhorse of control applications. In particular, the vast majority of current applications employ proportional-integral-derivative (PID) controllers. In the aerospace as well as process industries, PID control has proven to be easy to use and to provide adequate performance. PID controllers are also general purpose, that is, the same controller structure can be used for a broad range of applications.
Yet PID control is far from ideal. For any nontrivial application, we know that nonlinear controllers can substantially outperform a PID. For specific plants, high-performing nonlinear controllers can be designed. But, in practice, this has required unique designs for each enterprise, with concomitant high cost and complexity.
Neural Networks have recently been shown to provide a highly effective replacement or supplement for PID controllers, providing nonlinear control without the usual expense and complexity of such nonlinear control systems. U.S. Pat. No. 5,396,415 to Konar et al. for example, describes a control system which uses a neural network to supplement PID control. U.S. Pat. No. 5,159,660 to Lu et al. applies neural network technology as a stand-alone replacement for PID control. The applicant has discovered that the effectiveness and versatility of these systems may be advanced even beyond the contemplation of the authors of these references. As will be shown, a control system including a neural network using normalization techniques described herein will allow a trained neural network to be used in control applications other than the one it was trained for, with excellent results. The applicant's invention, also makes more effective use of the control devices used to alter the process by ensuring that full operating range of associated control devices are effectively used.
PID controllers are used ubiquitously in conventional control systems. As conventionally formulated, these PID controllers use six input signals to generate an output which drives the application process. The input signals represent on the one hand, controller parameters (or gains) K.sub.P, K.sub.I and K.sub.D and, on the other, three error signals or process condition signals: the error between the setpoint or reference model response and the process response, e, the integral of this error, .intg.e, and the derivative of this error, e. This function computed by conventional PID controllers is a linear weighted sum of the error signals : EQU u.sub.PID =K.sub.P e+K.sub.I .intg.e+K.sub.D e
It may be computed either in analog or digital fashion to yield u.sub.PID. As indicated, K.sub.P, K.sub.I and K.sub.D are controller parameters, or gains. Their values uniquely determine controller response characteristics. In the conventional PID paradigm, it is assumed that by increasing the proportional gain K.sub.P, we can increase the closed loop bandwidth (reducing the time needed to attenuate disturbances); by increasing the derivative gain K.sub.D we can increase the damping (reducing overshoot): and by increasing the integral gain K.sub.I we increase the system robustness (reducing sensitivity to disturbances) and reduce steady-state tracking errors. The behavior of the closed loop system (dynamic system), however, does not always decouple in this way. That is, increasing integral gain may reduce damping, or increasing proportional feedback can increase sensitivity, etc. In practice, the user installs a PID controller box in a feedback loop and adjusts the gains until the closed loop response of the system is a good compromise among the user's competing objectives.
There is no theoretical reason to believe that this is the optimal function of these six quantities. In fact, in many applications, it is unlikely to be the optimal solution, since the optimal solution is non-linear, or a series of linear solutions, optimal for a given range of conditions. Therefore, conventional PID controllers are not as good as they could be if the larger search space of linear and nonlinear functions was available for control solutions.
The neural network provides a way of searching through a larger solution space for the best possible control solution. In a similar manner to the PID controller, the neural network is provided with input stimulus, and the weights internal to the neural network are adjusted to achieve a good compromise among the user's competing objectives. Since the neural network is not limited to linear solutions for the controller response, a significantly larger number of solutions are available for controlling the process.
The ubiquitous use of linear control systems to adequately provide control solutions suggests that they at least do a fair job of control in many applications. In these cases, the PID may simply need a supplemental device, such as a neural network, to "tweak" the PID result. In other cases, a given application may have linear and nonlinear areas of operation, and in these cases, the PID controller and the Neural Network may alternately dominate the process control, based on the characteristics of the control situation. In still other cases, the application to be controlled will have very little linear characteristics, and thus a stand-alone neural network may provide the best control solution. Regardless of the control arrangement in which the neural network operates in however, PID parameters provide a useful means to describe system activity and performance.
In either a combination PID/ neural network system, or a straight PID system, signals which reflect the state of the process, or process condition signals .sub.(e, .intg.e,e), may not be uniform in magnitude, and may vary both positive and negative. Ideally, the neural network should be capable of compensating for these weight differences by sufficient training. In reality, a neural network may not be trained indefinitely, and eventually reaches a point of diminishing returns. If the weights of the neural network do not compensate for the magnitude differences during this time, an imperfect control solution may occur. Furthermore, training performed for one type of control environment will be tailor-made for that environment because of the arbitrary weights. The trained neural network will perform poorly when used for another control application unless the range of the process variables in the new control application is similar to that of the control application the neural network was trained with.
Proper normalization for neural network input signals simplifies the neural network's task, and consequently improves its ability to learn how to control. Thus, a controller providing the best possible control solution, and capable of performing effectively in control applications other than the one it was trained for is achieved. Normalization also allows the most effective utilization of the control devices used to alter the process by maximizing their full range of operation. Overall, we show that neural networks can provide some of the most versatile, effective nonlinear control systems presently available.
Versatility in a control system is almost always a benefit to a control system designer. The applicant's invention will allow the designer to contemplate use of a single controller for numerous applications, without requiring training for each application. It may even allow simultaneous use of a single control system for numerous applications, having substantially different non-linear characteristics. In principle, existing systems can even be retrofitted with the applicant's system, requiring no retraining, and, in fact, in many cases may produce better control results than the original control system.